software engineers in scientific computing

Abstract: We present Cyclotron, a compiler that expresses streaming dataflow algorithms using recurrence equations, which are then compiled to distributed topologies of interlinked processors. Our compiler lowers a language of recurrences over logical iteration spaces into per-processor programs of sends, receives, and computations. In these recurrences, data accesses are not limited to external accesses to memory; data can live separately on the iteration space itself, allowing internal points to communicate values directly with other points. Users specify this communication directly in the recurrence language, which allows them to express various communication patterns such as a nearest-neighbor systolic exchange, a one-to-all broadcast, a bidirectional split ring, or an asymmetric and piecewise broadcast pattern, which are often not supported by standard distributed linear algebra libraries. These recurrences describe the algorithm and communication independently of how they map onto the hardware. A programmer then chooses which dimensions execute across processors and which execute over time, without rewriting the entire program. Users only specify data dependencies across the iteration space, and the compiler safely generates a program, per process, with correct placement of both communication and computational operators according to the chosen space--time mapping. We evaluate distributed matrix multiplication, TRSM, Cholesky, and fused Cholesky--TRSM on up to 16 CPU nodes and 16 GPUs, comparing against ScaLAPACK, SLATE, and cuSolverMp. Cyclotron is competitive with and often outperforms these hand-optimized libraries; for Cholesky, the best communication strategy changes with problem size and architecture.

Abstract: Machine learning surrogates of partial differential equations (PDEs) are commonly trained on data generated by numerical solvers. Therefore, the training data obey not the PDE but the modified equation of the numerical scheme, and the test loss, computed on data from the same solver, cannot distinguish a model that learned the physics from one that learned the discretization error. Here, we show that the difference is nevertheless visible in the trained model. We propose a suite of structure-preserving fidelity diagnostics, simple scores that measure whether a learned model respects one known property of the physics, such as a conserved quantity, a symmetry or a Hamiltonian structure, without access to the training data or the governing equation. Over five systems, the diagnostics track the error with respect to the true dynamics with a rank correlation of up to $0.94$, while the test loss is uncorrelated or anti-correlated with it. For the Burgers, Korteweg-de Vries and Navier-Stokes equations, the diagnostics separate numerical schemes that the test loss ranks as equivalent, including schemes of the same order. order.

Abstract: Multiphysics continuum models are powerful tools for studying electrochemical devices, enabling in silico reactor design and resolution of local pH, potential, and concentration fields that govern device performance but are difficult to measure experimentally. However, constructing such models requires substantial numerical expertise or reliance on proprietary software. Here, we show that frontier large language model agents can remove this implementation burden while keeping the underlying physics under researcher control. Using one-dimensional electrochemical CO2 reduction to CO in a porous gas diffusion electrode as a test case, we develop a machine-readable, human-specified modeling harness containing governing equations, parameters, numerical methods, logical build stages, and human-verifiable checkpoints. From this specification, the agent reproducibly constructs complete multiphysics models in open-source Julia. Independently built models, including fully autonomous agent-built models, agree with an equivalent COMSOL implementation to within 0.7% of the peak CO partial current density, and with one another to within 0.04%. Systematically planted errors demonstrate the importance of explicit specifications for reproducibility and reveal the agent's capabilities and limitations in debugging model physics. This framework establishes a more transparent approach to multiphysics modeling in which physical descriptions and governing equations, rather than specialized code, become the primary inputs for computational model development.

Abstract: AI could change which parts of science impede progress. Consider a world in which machine systems are better, faster, and cheaper than people at most scientific work that can be done through a computer. Our question is what would limit science in that world. Literature synthesis, hypothesis generation, software development, simulation, and analysis could become abundant, while experiments, observations, well-supported conclusions, and accountable institutional au- thority remain scarce. Science would then be constrained by a different set of resources. In this paper, we call this change the scarcity inversion and consider four parts of it: selection, physical access, validation, and organizational choice. This change is arriving first in mathematics and coding/software/algorithm design, where the whole scientific loop can run inside computation. For national laboratories, the change could be striking. Their distinctive role is to turn abundant machine reasoning into trustworthy results by combining controlled experiments, protected data, expert judgment, and accountable authority. The practical question is how facilities, verification, provenance, resource allocation, and scientific governance should change when reasoning is plentiful and trustworthy evidence is scarce.

Abstract: Discovering underlying symmetries from data has emerged as a crucial challenge in scientific discovery. Existing data-driven methods for symmetry discovery fail to determine the exact number and mathematical form of unknown infinitesimal generators. Recent explicit methods represent generators using a predefined function library and identify them through algebraic optimization, but they often struggle to capture complex symmetries involving high-order polynomials or transcendental functions. To address this limitation, we formulate symmetry discovery as a joint optimization problem over the function library and coefficients. We propose a novel framework that leverages an encoder-decoder architecture to dynamically generate symbolic expressions and expand the library. This generation process is optimized via reinforcement learning, which accelerates the exploration of the symbolic search space through step-wise rewards. Experiments demonstrate that LieDiscover can successfully uncover open-form infinitesimal generators involving high-order polynomials or transcendental functions, which remain intractable for existing methods. The discovered symmetries also improve performance in downstream PDE solving and discovery tasks.